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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

Working out climate sensitivity from satellite measurements

What the science says...

Lindzen's analysis has several flaws, such as only looking at data in the tropics. A number of independent studies using near-global satellite data find positive feedback and high climate sensitivity.

Climate Myth...

Lindzen and Choi find low climate sensitivity
Climate feedbacks are estimated from fluctuations in the outgoing radiation budget from the latest version of Earth Radiation Budget Experiment (ERBE) nonscanner data. It appears, for the entire tropics, the observed outgoing radiation fluxes increase with the increase in sea surface temperatures (SSTs). The observed behavior of radiation fluxes implies negative feedback processes associated with relatively low climate sensitivity. This is the opposite of the behavior of 11 atmospheric models forced by the same SSTs. (Lindzen 2009)

Climate sensitivity is a measure of how much our climate responds to an energy imbalance. The most common definition is the change in global temperature if the amount of atmospheric CO2 was doubled. If there were no feedbacks, climate sensitivity would be around 1°C. But we know there are a number of feedbacks, both positive and negative. So how do we determine the net feedback? An empirical solution is to observe how our climate responds to temperature change. We have satellite measurements of the radiation budget and surface measurements of temperature. Putting the two together should give us an indication of net feedback.

Lindzen et al also analysed satellite measurements of outgoing radiation over these periods. As short-term tropical sea surface temperatures are largely driven by the El Nino Southern Oscillation, the change in outward radiation offers an insight into how climate responds to changing temperature. Their analysis found that when it gets warmer, there was more outgoing radiation escaping to space. They concluded that net feedback is negative and our planet has a low climate sensitivity of about 0.5°C.

Debunked by Murphy

Another major flaw in Lindzen's analysis is that they attempt to calculate global climate sensitivity from tropical data. The tropics are not a closed system - a great deal of energy is exchanged between the tropics and subtropics. To properly calculate global climate sensitivity, global observations are required.

This is confirmed by another paper published in early May (Murphy 2010). This paper finds that small changes in the heat transport between the tropics and subtropics can swamp the tropical signal. They conclude that climate sensitivity must be calculated from global data.

Debunked by Chung

In addition, another paper reproduced the analysis from Lindzen et al 2009 and compared it to results using near-global data (Chung et al 2010). The near-global data find net positive feedback and the authors conclude that the tropical ocean is not an adequate region for determining global climate sensitivity.

Debunked by Dessler

Dessler (2011) found a number of errors in Lindzen and Choi (2009) (slightly revised as Lindzen & Choi [2011]). First, Lindzen and Choi's mathematical formula to calculate the Earth's energy budget may violate the laws of thermodynamics - allowing for the impossible situation where ocean warming is able to cause ocean warming. Secondly, Dessler finds that the heating of the climate system through ocean heat transport is approximately 20 times largerthan the change in top of the atmosphere (TOA) energy flux due to cloud cover changes. Lindzen and Choi assumed the ratio was close to 2 - an order of magnitude too small.

However, Dessler also plots climate model results and finds that they also simulate negative time regression slopes when cloud changes lead temperature changes. Crucially, sea surface temperatures are specified by the models. This means that in these models, clouds respond to sea surface temperature changes, but not vice-versa. This suggests that the lagged result first found by Lindzen and Choi is actually a result of variations in atmospheric circulation driven by changes in sea surface temperature, and contrary to Lindzen's claims, is not evidence that clouds are causing climate change, because in the models which successfully replicate the cloud-temperature lag, temperatures cannot be driven by cloud changes.

Lindzen and Choi first submitted LC11 to the Proceedings of the National Academy of Sciences (PNAS) after adding some data from the Clouds and the Earth’s Radiant Energy System (CERES).

PNAS editors sent LC11 out to four reviewers, who provided comments available here. Two of the reviewers were selected by Lindzen, and two others by the PNAS Board. All four reviewers were unanimous that while the subject matter of the paper was of sufficient general interest to warrant publication in PNAS, the paper was not of suitable quality, and its conclusions were not justified. Only one of the four reviewers felt that the procedures in the paper were adequately described.

As PNAS Reviewer 1 commented,

"The paper is based on...basic untested and fundamentally flawed assumptions about global climate sensitivity"

Assuming that that correlations observed in the tropics reflect global climate feedbacks.

Focusing on short-term local tropical changes which might not be representative of equilibrium climate sensitivity, because for example the albedo feedback from melting ice at the poles is obviously not reflected in the tropics.

Inadequately explaining methodology in the paper in sufficient detail to reproduce their analysis and results.

Failing to explain the many contradictory results using the same or similar data (Trenberth, Chung, Murphy, and Dessler).

Treating clouds as an internal initiator of climate change, as opposed to treating cloud changes solely as a climate feedback (as most climate scientists do) without any real justification for doing so.

As a result of these fundamental problems, PNAS rejected the paper, which Lindzen and Choi subsequently got published in a rather obscure Korean journal, the Asia-Pacific Journal of Atmospheric Science.

Wholly Debunked

A full understanding of climate requires we take into account the full body of evidence. In the case of climate sensitivity and satellite data, it requires a global dataset, not just the tropics. Stepping back to take a broader view, a single paper must also be seen in the context of the full body of peer-reviewed research. A multitude of papers looking at different periods in Earth's history independently and empirically converge on a consistent answer - climate sensitivity is around 3°C implying net positive feedback.

Further viewing

Comments

If the cloud feedbacks are indeed positive and inline with the IPCC model predictions of about a 3 C rise in temperature from a doubling of CO2 (a 3.7 W/m^2 gross increase in radiative forcing; 1.85 W/m^2 net), then why doesn’t the same proportional amount of positive feedback amplification lead to 16+ C rise in temperature when the net albedo adjusted incident solar power at perihelion is about 14 W/m^2 higher?
Instead, average global temperatures are actually colder at perihelion in January then at aphelion in July.

What is so special about 1 W/m^2 of additional power from CO2 that it’s at least 5 times more powerful than 1 W/m^2 of additional power from the Sun?

However the answer to your question is that CO2 adds the heat all the time, year after year (think of a bathtub filling), whereas changes during a year cancel out over longer timescales (think of waves in the bathtub).

Then how do you explain the relatively large and fast seasonal temperature changes that occur in each hemisphere every year? The seasonal hemispheric fluctuations in radiative forcing that occur are astronomically greater than the measly 1.85 W/m^2 that will come from a doubling of CO2. If what you’re saying is true, we wouldn’t see anywhere near the seasonal variability that occurs each year.

(*The peak to peak difference in solar radiance between perihelion and aphelion is about 80 W/m^2. Divide by 4 to get the average of 20 W/m^2, then subtract out the albedo of about 0.3 and you get a net increase of about 14 W/m^2 at perihelion.

The average incident solar energy is about 340 W/m^2. If you subtract the effect of the earth’s albedo (about 30% or 0.3 = 102 W/m^2), you get a net incident solar energy of about 238 W/m^2 (340 – 102 = 238). (*The albedo is the amount of incoming short wave radiation from the sun that gets reflected back out to space off of clouds, snow, ice, etc., and cannot be absorbed by GHGs or contribute to the greenhouse effect, which is why it’s subtracted out).

From this you take the surface power at the current average global temperature of 288K, which is about 390 W/m^2 (from Stefan Boltzman), and with it you can calculate the gain or the amount of surface warming as a result of the greenhouse effect in the atmosphere. To get this you divide the current surface power by the net incident solar power, which comes to about 1.6 (390/238 = 1.6). What this means is that for each 1 W/m^2 of solar input, you get 1.6 W/m^2 of power at the surface due to the presence of GHGs and clouds in the atmosphere – a boost of about 60%.

A doubling of CO2 alone absorbs only about 4 W/m^2 of additional power. About half this is directed upward out to space and the other half is directed downward toward the surface, resulting in a net of about 2 W/m^2. If you then multiply this additional 2 W/m^2 of power by the same gain calculated for solar power (as a result of the greenhouse effect), you get an increase in the surface power of about 3.2 W/m^2 from a doubling of CO2 (2 x 1.6 = 3.2). Using Stefan Boltzman, an additional 3.2 W/m^2 will increase the surface temperature only about 0.6 degrees C (390 + 3.2 = 393.2 W/m^2 = 288.6K). This is much less than the 3 degrees C predicted by the IPCC. Even if you assume all of the 4 W/m^2 from a doubling of CO2 goes to the surface, the temperature increase would still only be 1.2 degrees C – significantly less than the low end of the IPCC’s claimed range of 2 – 4.5 C.

To get the 3 degrees C claimed by the IPCC, an additional 16 W/m^2 would be needed. This requires a gain of 8 rather than 1.6 (or at least a gain of 4 instead of 1.6 if we assume all of the absorbed power is directed back to the surface). The bottom line is the actual response of atmosphere (from GHGs and clouds) relative to net incident solar power, measured in W/m^2, is far less than the response claimed by the IPCC from a doubling of CO2, which is also measured in W/m^2. A watt/meter squared of heat and power is watt/meter squared of heat and power, independent of where it originates from – whether it’s the Sun, or redirected back to the surface as a result of more CO2 in the atmosphere (*If this was not true, then power from the Sun and additional power from CO2 cannot both be expressed in W/m^2 as they are). Ultimately, the total power flux at the surface is directly tied to temperature via Stefan-Boltzman - there is no escaping this.

In short, the surface gain factor of about 1.6 supports an upper limit of only about 0.6 C from a doubling of CO2 because there is no physical or logical reason why a small increase of less than 2 W/m^2 will behave radically differently than the original 99+ percent - i.e. a gain of 8 or more needed for a 3 C rise is simply way outside the bounds of empirically derived observations of how the system responds to changes in radiative forcing.

RW1
if you wish to (even roughly) calculate the result of an energy (im)balance you have to do it at the top of the atmosphere (TOA). You can not take two different pieces, at surface and at TOA, and mix them together.

You need to be more specific - I'm not sure what you're trying to say.

The halving of the CO2 absorption is because the re-radiated energy goes out in all directions - meaning half is radiated upward in the same general direction it was already headed; thus it cannot contribute to additional warming.

RW1
you first calculated a sort of energy balance at the earth surface to calculate the "amplification factor"; then you took the (net) energy imbalance at TOA, the 4 W/m2 for doubling CO2, and used the same "amplification factor" to calculate the extra energy received by the surface and the increase in temperature.

I'm asking the question because I think it's a significant hole in the AGW theory that I've yet to see adequately explained.

What I'm trying to show is that the CO2 AGW theory is saying that the climate system is all of the sudden going to treat an additional 2 W/m^2 of power at the surface radically different than it does the original existing 99+ percent, and while I suppose that is theoretically possible, there is no physical, empirical or logical reason why it would, especially in a system that is constantly changing everywhere, by relatively large magnitude.

Ultimately, what matters is the total infrared power at the surface, independent of where all the power orginates from - the the Sun, GHGs and/or clouds. Both 2 W/m^2 of additional infrared power from the Sun "forcing" the surface and 2 W/m^2 of additional infrared power from CO2 "forcing" the surface are the same - all the surface 'knows' is what the total power is, and the total power is directly tied to temperature via Stefan-Boltzman (*if this was not true, then power from the Sun and additional power from CO2 cannot both be expressed in W/m^2 as they are).

The point I was making about the perihelion power increase of about 14 W/m^2 was that a much larger increase in radiative forcing above the average doesn't have anywhere near the proportionally predicted effect as the AGW warming theory says will happen with just a 2 W/m^2 increase in radiative forcing from a doubling of CO2. Now of course one can always say that it will be the 2 W/m^2 increase above the total cumulative average that will cause a much larger amount of warming by suddenly triggering very large positive feedbacks (that don't happen to exist or act on the original 99+%), but there really isn't any physical, logical, or empirical basis for that, especially given the total amount of radiative forcing is constantly changing spatially and in time...all the time (warming, cooling, etc). If the climate as a whole was a steady state and static system, it might be more plausible, but the climate system is incredibly dynamic instead.

That the global climate doesn't even appear to be phased by a 14 W/m^2 increase in radiative forcing, suggests the net feedback operating on the system as a whole is strongly negative - not positive, and the tiny increase of only about 2 W/m^2 from a doubling of CO2 will be - if not infinitesimal, benignly small.

"All I did was apply the same gain factor for solar power to additional power from CO2."
You did it wrong as I explained in my previous post, you're confusing surface and TOA.

"Ultimately, what matters is the total infrared power at the surface"
The energy balance of the planet is governed by what happen at TOA, not at the surface. What we see (measure) at the surface is the effect of the change at TOA.

"The point I was making about the perihelion power increase of about 14 W/m^2 was that a much larger increase in radiative forcing above the average doesn't have anywhere near the proportionally predicted effect as the AGW warming theory says will happen with just a 2 W/m^2 increase in radiative forcing from a doubling of CO2." (emph. mine)
You should not expect any proportionality, indeed. When you have a cyclic forcing, the effect depends of the response time of the system. If the response is slow you won't get the full effect of the forcing; you are comparing a forcing with a one year period with a response time of the order of decades. An extreme example is the diurnal cycle, where you have the forcing going from about 240 W/m2 to zero but the temperature doesn't change proportionally.

How am I confusing the surface and the TOA? Are you saying that power from the Sun and additional power redirected from CO2 are not both "forcing" the surface?

The energy balance is determined by the rate at which incoming power from the Sun is allowed to leave the planet (at the TOA):

The incoming short wave infrared energy from the Sun is mostly transparent to the clear sky atmosphere. Cloudy sky is obviously different, as a lot of the energy is reflected off of and absorbed by the clouds - a much smaller amount makes it through. The short wave energy that hits the surface is re-radiated back up in the form of long wave infrared, which in certain wavelengths is absorbed and re-radiated by greenhouse gases and/or clouds. In effect, the presence of greenhouse gases and clouds delay the release of infrared heat energy by redirecting some of it back toward the surface, which makes the surface warmer than it would be otherwise.

The albedo adjusted gain factor of about 1.6 means that due to the greenhouse effect, it takes about 1.6 W/m^2 of power at the surface for each 1 W/m^2 of power to leave the system, offsetting each 1 W/m^2 entering the system from the Sun. In other words, power in = power out. The albedo adjusted solar input of about 238 W/m^2 = 238 W/m^2 leaving the planet, and a power of 238 W/m^2 equates to a temperature of about 255K, which is the so-called effective temperature of the earth as seen from space.

There is no difference between power sourced from the Sun and additional power re-directed back to the surface as a result of more CO2 being added to the atmosphere. Afterall, a watt/meter squared of energy and power is watt/meter squared of energy and power, independent of where it originates from. Put another way, the surface doesn't "know the difference" between heat or power sourced from the Sun or additional heat or power re-directed back down from GHGs and/or clouds - all it "knows" is what the total heat and power is at the surface; and the total power at the surface in W/m^2 is directly tied to temperature via Stefan-Boltzman because the surface of the earth is considered to be very close to a perfect black body radiator.

At an average global temperature of 288K, the surface emits 390 W/m^2 of power. About 240 W/m^2 of this is from the Sun and the additional 150 W/m^2 is from GHGs and clouds in the atmosphere re-directing infrared power back down toward the surface. If the albedo adjusted power from the sun increases 2 W/m^2, the infrared power at the surface increases 2 W/m^2, plus about an additional 1.2 W/m^2 will be redirected back downward from the atmosphere (due to the presence of GHGs and clouds) for net increase of about 3.2 W/m^2 - raising the surface power total to about 393.2 W/m^2 (or a temperature of 288.6K). If instead, the albedo adjusted power from the Sun is unchanged, but an additional 2 W/m^2 of infrared power is redirected downward to the surface as a result of a doubling of CO2, the most additional power that can amplify (or in effect re-redirect down) the added 2 W/m^2 is only about the same 1.2 W/m^2 because there is no physical or logical reason why an additional 2 W/m^2 of infrared power at the surface will behave radically different from either the original 99+% or an additional 2 W/m^2 from the Sun.

The hemispheric seasonal responses to large changes in radiative forcing are relatively quick – certainly not years or decades. If they were, we wouldn't see anywhere near the seasonal variability throughout each year. There is a delay or "seasonal lag", but it’s only about one month.

This contradicts the notion that a tiny increase in radiative forcing of less than 2 W/m^2 from a doubling of CO2 gradually added to atmosphere over decades will take decades longer after to reach equilibrium. If anything, because CO2 is added incrementally and so slowly over such a long period of time, the response time is a non issue.

Yes, the oceans have thermal inertia, as evidenced by the roughly one month of "seasonal lag", but the overall response is still relatively fast in each hemisphere every year. This contradicts the ocean thermal inertial taking decades to fully respond.

The albedo adjusted gain is just an aggregate empirical measure of the system's response at the surface to incoming power from the Sun. As you can see from that site, it varies a little but is roughly about 1.6 on average.

RW1
the often quoted 4 W/m2 is the imbalance at TOA, i.e. the amount of energy not allowed to leave the planet after a doubling of CO2. Following your scheme, an equal amount is radiated back to the surface. In this way you get a 1.2 K increase in temperature; incidentally, this is equal to the so-called Plank sensitivity. To know the equilibrium temperature increase you still need to multiply it by the feedback factor, which is not included in the 4 W/m2.

4 W/m^2 would the total that affects the surface only if all the absorbed power is directed back toward the surface, but only about half of it does because GHG infrared absorption and re-radiation is in all directions - i.e. about half goes down and other half goes up out to space in the same general direction it was already headed.

You can't assume all the increase in temperature we've seen is from additional CO2. The climate doesn't do anything but change. There are many natural forces at work, the bulk of which we don't even know.

@RW1: sure we can assume the warming is due to CO2, because there are no other causes that could be indentified. Of course, this means filtering out cyclical patterns, which is what climate scientists do.

That said, if you want to chase for those elusive other causes, please do, and come back to us when you have actual evidence. In the meantime, we'll stick with the actual science.

The burden of proof is not on the skeptics to demonstrate what caused the warming because the amount and rate of warming we've experienced is well within the range of natural variability.

The burden of proof is on the AGW proponents to demonstrate it was caused by CO2, and all of that evidence has to be in accordance with all other existing evidence. There can't be any significant discrepancies or inconsistencies, especially those which cannot be adequately explained in the overall context of the theory. It only takes one piece of contradictory evidence to disprove a hypothesis - no matter how much confirming evidence may exist.

Now I know that climate is not an exact science, so there is some leeway; however, these basic fundamental scientific principles still apply.

#29: "It only takes one piece of contradictory evidence to disprove ... "

Where is this piece of evidence? Love to see it.

Let's review what we have seen: Begin with this quixotic statement: "... average global temperatures are actually colder at perihelion in January then at aphelion in July." Follow with some back-of-the-envelope-style calculations which some here have already called into question. Continue with the declarative judgment "response time is a non issue". Avoid all attempts to consider other SkS pages wherein these claims, many of which have been raised before, are addressed in detail.

@RW1: "The burden of proof is not on the skeptics to demonstrate what caused the warming because the amount and rate of warming we've experienced is well within the range of natural variability."

Wrong. The burden of proof *is* on the skeptics to prove that similar temperature increases have happened at this rate in the past, and that similar natural forces are at play today. There is no evidence of this, nor have you provided any.

"The burden of proof is on the AGW proponents to demonstrate it was caused by CO2, and all of that evidence has to be in accordance with all other existing evidence."

Wrong again. The burden of proof is on the AGW proponents to demonstrate it was caused by CO2, and all of that evidence has to be in accordance with all other existing evidence.

The evidence is already there supporting AGW, if only in the satellite-measured OLR or ground-measured downward LR. In other words, all lines of evidence point to the warming being caused by CO2, while there is virtually no evidence supporting your position.

"It only takes one piece of contradictory evidence to disprove a hypothesis - no matter how much confirming evidence may exist."

As muoncounter said, please provide this evidence. After all, the burden of proof is on you, not on AGW proponents.

AGW is the currently accepted science. The burden of proof is on the challengers.

The biggest piece of contradictory evidence is that the amount of expected warming is absent. Due to the logarithmic response of CO2, an increase from 280 ppm to 380 ppm equals about 75-80% of the forcing from a doubling of CO2. 75% of 3 degrees C is 2.25 degrees C. During the period from about 1900-2000, the amount of warming was only about 0.6 C - less than 1/3rd of the predicted amount, and that's only if you assume all the warming was from CO2 (highly unlikely).

They have tried, after the fact, to ascribe the lack of warming to be due to aerosols. Or is it ocean thermal inertia? Or something different tomorrow or next week? It seems anything but conclude the hypothesis is probably wrong, and the sensitivity is far smaller than they are still claiming it is.

The scientific method dictates modifying or discarding a hypothesis when it does not fit the evidence. It does not permit adding unsubstantiated things arbitrarily after the fact when the hypothesis is not in accordance with the evidence.

The site that was referenced and the empirically derived calculations of sensitivity by George White totally add up. I've never seen the fundamental science, calculations and logic presented there adequately disputed anywhere. If you believe you have clear evidence that contradicts it, present it in detail and we'll discuss and debate it.

Just look at the icecore data from Vostok, for example. The amount of warming we've experienced in the last 100 years of about 0.6 degrees C is not only within the range of natural variability - it's below average. Over the last 10,000 years the average amount of temperature change per century is roughly 1 degree C - with some 100 year periods seeing as much as 2 degrees C:

First, most of the CO2 has been added to the atmosphere in the past 40 years.

Second, it takes quite a while for the entire impact of CO2 to be felt, so some of that temperature increase is still "in the pipeline."

Third, I don't believe you get 75% of the increase you'd get from doubling CO2 from a 35% increase in its concentration. I'd be curious to see where you got those figures - hope it's not from that same website.

Fourth, the current temp increase is 0.8C, not 0.6C.

"and that's only if you assume all the warming was from CO2 (highly unlikely)"

CO2 + Feedbacks. It's not "highly unlikely", but rather very likely that the greater part of the warming is due to CO2 increase, and you have not provided any evidence to the contrary.

"I've never seen the fundamental science, calculations and logic presented there adequately disputed anywhere."

May I suggest that you actually look at peer-reviewed litterature rather than seeking confirmation for what you already believe from random web sites on the Internet?

RW1 writes: "Due to the logarithmic response of CO2, an increase from 280 ppm to 380 ppm equals about 75-80% of the forcing from a doubling of CO2."

Forget about learning the science... you aren't going to get anywhere until you learn math.

ln(380/280)=0.305382, or about 31%... not 75-80%

Also: "75% of 3 degrees C is 2.25 degrees C."

Which, in addition to the incorrect starting factor, would assume that all the warming feedbacks were instantaneous... which is not what climate science projects. It will take decades after any given CO2 level is reached for all the FAST feedbacks to play out and centuries for slow feedbacks to complete.

Also: "During the period from about 1900-2000, the amount of warming was only about 0.6 C"

The CO2 level at 1900 was higher than 280 ppm... so you are also using different base periods for your calculations of percentage increase of CO2 vs warming purportedly caused by this percentage increase.

Finally: "...less than 1/3rd of the predicted amount, and that's only if you assume all the warming was from CO2 (highly unlikely)."

The figure of 3C from a doubling of CO2 you cite is the amount climate science projects from CO2 and fast feedbacks not CO2 alone.

If you correct for the host of errors identified above you will find that based on the increase of CO2 levels observed so far we'd expect, and have observed, temperature increases of about 0.8 C globally since CO2 rose above 280 ppm. In short, projections of 3 C warming are right on track... which is precisely why that IS the average projection... because it is what observations thus far suggest is most likely.

@RW1: cherry-picking. That graph is for a single region, not a global average. It is well known certain areas see greater variability, especially near the poles. For example, the current Arctic anomalies are more than twice the global one (which is 0.8, not 0.6), putting them in the high end of what this graph shows. Never mind the fact that most of the warming has occured over the last 40 years, not century.

Nice try, but this has been debunked here countless times. Perhaps you should actually learn the science on this site before arrogantly claiming to overturn decades of climate science with your old and tired talking points?

I know the feedbacks are not included in the 4 W/m^2 (2 W/m^2 net) - that is why the actual response is greater than 2 W/m^2 or about 3.2 W/m^2 (or 6.4 W/m^2 if all the absorbed power is assumed to be directed back to the surface). The point is even if all the power is directed back down, the temperature increase would still only be about 1.2 C, which is significantly less than the 3 C predicted (390 W/m^2 + 6.4 W/m^2 = 396.4 W/m^2 = 289.2K).

No one has yet to really address the initial question, which is what's so special about 1 W/m^2 additional of power from CO2 that the system is all of the sudden going to treat it as being at least 5 times more powerful than 1 W/m^2 of power from the Sun?

"4 W/m^2 would the total that affects the surface only if all the absorbed power is directed back toward the surface, but only about half of it does because GHG infrared absorption and re-radiation is in all directions - i.e. about half goes down and other half goes up out to space in the same general direction it was already headed"

I have already pointed out twice that this is simply plain wrong. The point on emissions being both up and down is irrelevant - the calculation already takes account of the fact that emission is isotropic.

The response of incrementally more CO2 is not linear - but logarithmic, which means each additional amount added only has about half of the effect of the previous amount.

This is how and why I'm getting about 75-80% when going from 280 ppm to 380ppm. What this also means is that the remaining 180 ppm to get to a doubling of 560 ppm will only have about 20-25% of the effect as the first 100 ppm

RW1
no one addressed your question because it makes no sense. As I'm trying to explain your reasoning is wrong beacuse you mix what happens at TOA with what happens at the surface. You should work out the correct energy balance starting with a simple zero-dimensional model.

As I pointed out in another thread quoting Mombiot, I'm afraid that some trolling need to be taken into account. The obstinacy in certain errors and the conceitedness of having found a "significant hole in the AGW theory" with a few (wrong) back of the envelop calculations are typical; the tactics in the dicussion are also always the same. Sound familiar.

Explain to me what is happening at the TOA vs. what is happening at the surface. I need some specifics.

I understand that an imbalance at the surface from a increase in radiative forcing will be offset by radiating out more power at the TOA to compensate - to achieve equilibrium. Is this what you're saying?

I'm sticking to the science via civil discourse. And for the record, I don't believe that the 2nd law of thermodynamics contradicts the greenhouse effect or global warming theory at all.

I don't dispute that increased CO2 likely has some warming effect - I'm just presenting empirically derived evidence and logic that suggests the magnitude of the warming predicted - 3 degrees C, is simply much too high.

Can I say I am confused about what is actually being argued about here? A TOA energy imbalance implies earth is storing energy - this make future temperature rise inevitable but surely this is information about current energy imbalance.

Since 1750, top of tropopause downward radiative forcing is 2.9W/m2 due to change in GHG composition. Would this be the more relevant number?

Vostok is in Antarctica - not the Arctic, which I know is more variable than global averages. Antarctica is considerably less variable than the Arctic. Even if you assume the global averages were only half of what Vostok depicts, that still means the amount of warming we've seen is only about average or maybe a little above.

The 0.6 C rise was from 1900-2000 (i.e. 100 years), not necessarily the total rise since we've been measuring, which I don't doubt is about 0.8 C.

You can calculate the warming expected at equilibrium from an increase in atmospheric [CO2], very simply:

delta T = (ln([CO2]final/[CO2]start))*S/ln(2)

where delta T is the change in temperature at equilibrium from increasing atmospheric [CO2]start to [CO2]final, for a climate sensitivity of S (oC per doubling of [CO2]).

For your 280 ppm to 380 ppm, the warming at equilibrium for a climate sensitivity of 3 oC, is:

1.31 oC

The temperature rise from the period when [CO2] was 280 ppm (early-mid 19th century)[***] to 2000 is around 0.9 oC.

Since the Earth has a substantial inertia to warming, we certainly haven't attained equilibrium with respect to warming from the enhanced greenhouse forcing. Likewise we know that a significant amount of the warming from enhanced greenhouse forcing has been offset by anthropogenic aerosols. The solar contribution to warming is known to be small over this period (no more than 0.1 oC); note that a small part of the warming is from non-CO2 anthropogenic sources (methane, and nitrous oxides).

for a climate sensitivity of 2 oC the expected temperature rise is 0.88 oC. This is a small part of the reason that climate sensitivites below around 2 oC are simply incompatible with empirical observation. In other words we've already had the warming expected from a climate sensitivity of 2 oC, without taking into account the climate inertia and the effects of aerosols.

The empirical data are generally consistent with a climate sensitivity near 3 oC (per doubling of atmospheric [CO2].

[***] you have mismatched 280 ppm with 1990. In fact in 1990 atmospheric [CO2] was already near 300 ppm (297-298 ppm; see D. M. Etheridge et al (1996) "Natural and anthropogenic changes in atmospheric CO2 over the last 1000 years from air in Antarctic ice and firn J. Geophys Res. 101, 4115 -4128), and your expected temperature rise should be 1.02 oC for a climate sensitivity of 3 oC (we had around 0.75-0.8 oC of this to 2000...)